Prime numbers are numbers that are only divisible by themselves
and one. Ancient Greek mathematicians first studied them. Euclid
proved that there are infinite prime numbers. In the
"Fundamental Theorem of Arithmetic", Euclid prooved that
every integer can be written as a product of primes.
beginning of the 17th century, Fermat proved that every
prime number of the form 4n + 1 could be written as the sum of two
squares. Fermat also stated that the numbers 2n + 1 are
always prime if n is a power of 2. Numbers that have this property
were called Fermat numbers. After 100 years, Euler prooved
that this formula does not always work because 232 + 1
is equal to 4,294,967,297, which is not prime (it is divisible by
Marin Mersenne studied numbers of the form 2n –
1. They were named after him. Mersenne numbers were not
always prime. So far, 37 Mersenne numbers have been found.
The largest prime number is 23,021,377 - 1, which was
found by Ronald H. Clarkson, a sophomore at California State
University Dominguez Hills. The 37th Mersenne prime has
Some questions are still unanswered that relate to prime
- The Twin Primes Conjecture that there are infinitely
many pairs of primes only 2 apart.
- Goldbach’s Conjecture that every integer greater
than two can be written as the sum of two primes.
- Are there infinitely many primes of the form n2 +
- Is there always a prime between n2 and (n + 1)
- Are there infinitely many prime Fermat numbers?
- Are there infinitely long progressions of consecutive
- Are there infinitely many sets of three consecutive primes in
- n2 – n + 41 is prime for 0 £ n £ 40. Are there infinitely many primes
of this form?
- Are there infinitely many primes of the form n# + 1?
- Are there infinitely many primes of the form n# - 1?
- Are there infinitely many primes of the form n! + 1?
- Are there infinitely many primes of the form n! – 1?
- If p is prime, is 2P – 1 always square
- Does the Fibonacci sequence contain an infinite number of
1.) What is the sum of
the first 5 prime numbers?
2.) Which of the following is a prime
3.) How many primes are there that are less
4.) Which is not a prime number?
5.) A prime number is:
number that is only divisible by itself and one
number that is even and is divisible by 12 and 18
number that is odd
6.) Who was (or were) the first to study prime
ancient Greek mathematicians
7.) Fermat numbers are:
prime numbers that are even
prime numbers that were discovered by Fermat
prime numbers that have the property of 2n + 1 when n is
a power of 2